Josh Reyer corrected my interpretation of the Shinkage-ryu menkyo on Aikiweb. Somewhere. (I do believe the motivation, as I speculated, is unchanged).
But that correction does not creditably suggest that Takeda taught him Yagyu Shinkage-ryu. Why not?
1. Not one student of Takeda who demonstrates sword technique has an iota of YSR methodology.
2. If Ueshiba actually merited a menkyo in YSR, then a) why was his sword technique in the film in the 1930's so poor? And so un-Yagyu like.

We already know this. Gejo Kosaboro, a YSR exponent was Takeda Sokaku's student. He later became Ueshiba's student. (1925-30). He showed Ueshiba some Yagyu Shinkage-ryu, which Ueshiba experimented with ("in aiki, we do it this way"). His training partner was Tomiki Kenji. Later, he taught his adaptation of three kata to Hikitsuchi Morio. (Contemporary to his experimental adaptation of Kashima Shinto-ryu kata at Iwama).

My guess? Takeda felt that as Gejo was his student, he had a right to pass on such a menkyo (which is dubious as a menkyo in certain important respects, such as it having no lineage on it - something that is almost de rigueur.

And Hugh, all I'm saying is why not jump off established research to get something new, as opposed to ignoring such research and using long debunked "info" like that in Ratti and Wesbrook? The last chapter of my book was several pages of such suggestions - where would one go from here, so to speak - to find those missing pieces. No one has taken that next step in any of those research ideas. Instead, here we go backwards.